I already know the answers but please EXPLAIN how to get each answer, and show t

Question

I already know the answers but please EXPLAIN how to get each answer, and show the math.

You are on a spaceship traveling at 0.80c with respect to a nearby star sending a laser beam to a spaceship following you, which is moving at 0.50cin the same direction.

a) What is the speed of the laser beam registered by the second ship's personnel according to the classical addition of the velocities?

b)What is the speed of the laser beam registered by the second ship's personnel according to the relativistic addition of the velocities?

c)What is the speed of the second ship with respect to yours according to the classical addition of the velocities?

d) What is the speed of the second ship with respect to yours according to the relativistic addition of the velocities?

Explanation / Answer

given,

speed of first spaceship = 0.8c

speed of second spaceship = 0.5c

according to classical addition of the velocities

speed of the laser beam registered by the second ship's personnel = 0.8c - 0.5c

speed of the laser beam registered by the second ship's personnel = 0.3c

according to relativistic addition of the velocities

speed of the laser beam registered by the second ship's personnel = 0.8c - 0.5c / 1 - 0.8c * 0.5c / c^2

speed of the laser beam registered by the second ship's personnel = 0.5c

according to classical addition of the velocities

speed of the second ship with respect to first = 0.5c - 0.8c

speed of the second ship with respect to first = -0.3c

according to relativistic addition of the velocities

speed of the second ship with respect to first = 0.5c - 0.8c / 1 - 0.8c * 0.5c / c^2

speed of the second ship with respect to first = -0.5c

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